{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:DIXEU7H4YPOWL6NI3Y45XADBMK","short_pith_number":"pith:DIXEU7H4","schema_version":"1.0","canonical_sha256":"1a2e4a7cfcc3dd65f9a8de39db8061629c3c5cdf118b3f4a6baf8dc342010b78","source":{"kind":"arxiv","id":"2606.29662","version":1},"attestation_state":"computed","paper":{"title":"Fixed-parameter tractable computation of Reshetikhin--Turaev knot polynomials via tensor networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Shana Yunsheng Li","submitted_at":"2026-06-29T00:12:48Z","abstract_excerpt":"We give a thorough analysis of the time complexity of computing Reshetikhin--Turaev knot polynomials via tensor contractions on the associated tensor networks, showing that the computation is fixed-parameter tractable with respect to a parameter at most linear in the tree-width of the input knot diagram. When combined with existing approximation algorithms for tree decomposition, this recovers the sub-exponential bound $e^{O(\\sqrt{n})}$ for the time complexity of computing any Reshetikhin--Turaev knot polynomial. We accompany this paper with an implementation of such an algorithm in SnapPy, wh"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.29662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-06-29T00:12:48Z","cross_cats_sorted":[],"title_canon_sha256":"f08c3cda15a1b7be6d04316aa599e495704a9b630c268936b74b1d23406095b7","abstract_canon_sha256":"bc3b9776eced16c759e1a52ba7b73325dfccf9b6f903f94a56fb75b704120fef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:29.327194Z","signature_b64":"tMiqAr5zrNwrm2Sg/1LmMA96UM2hqncGM1Se7eKsG2Y5M3Vme7zms0UzYVW3IH7tMp2iOpdJFCoLwb8sbb2vBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a2e4a7cfcc3dd65f9a8de39db8061629c3c5cdf118b3f4a6baf8dc342010b78","last_reissued_at":"2026-06-30T02:17:29.326567Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:29.326567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fixed-parameter tractable computation of Reshetikhin--Turaev knot polynomials via tensor networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Shana Yunsheng Li","submitted_at":"2026-06-29T00:12:48Z","abstract_excerpt":"We give a thorough analysis of the time complexity of computing Reshetikhin--Turaev knot polynomials via tensor contractions on the associated tensor networks, showing that the computation is fixed-parameter tractable with respect to a parameter at most linear in the tree-width of the input knot diagram. When combined with existing approximation algorithms for tree decomposition, this recovers the sub-exponential bound $e^{O(\\sqrt{n})}$ for the time complexity of computing any Reshetikhin--Turaev knot polynomial. We accompany this paper with an implementation of such an algorithm in SnapPy, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29662","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29662/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.29662","created_at":"2026-06-30T02:17:29.326646+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.29662v1","created_at":"2026-06-30T02:17:29.326646+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29662","created_at":"2026-06-30T02:17:29.326646+00:00"},{"alias_kind":"pith_short_12","alias_value":"DIXEU7H4YPOW","created_at":"2026-06-30T02:17:29.326646+00:00"},{"alias_kind":"pith_short_16","alias_value":"DIXEU7H4YPOWL6NI","created_at":"2026-06-30T02:17:29.326646+00:00"},{"alias_kind":"pith_short_8","alias_value":"DIXEU7H4","created_at":"2026-06-30T02:17:29.326646+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DIXEU7H4YPOWL6NI3Y45XADBMK","json":"https://pith.science/pith/DIXEU7H4YPOWL6NI3Y45XADBMK.json","graph_json":"https://pith.science/api/pith-number/DIXEU7H4YPOWL6NI3Y45XADBMK/graph.json","events_json":"https://pith.science/api/pith-number/DIXEU7H4YPOWL6NI3Y45XADBMK/events.json","paper":"https://pith.science/paper/DIXEU7H4"},"agent_actions":{"view_html":"https://pith.science/pith/DIXEU7H4YPOWL6NI3Y45XADBMK","download_json":"https://pith.science/pith/DIXEU7H4YPOWL6NI3Y45XADBMK.json","view_paper":"https://pith.science/paper/DIXEU7H4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.29662&json=true","fetch_graph":"https://pith.science/api/pith-number/DIXEU7H4YPOWL6NI3Y45XADBMK/graph.json","fetch_events":"https://pith.science/api/pith-number/DIXEU7H4YPOWL6NI3Y45XADBMK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DIXEU7H4YPOWL6NI3Y45XADBMK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DIXEU7H4YPOWL6NI3Y45XADBMK/action/storage_attestation","attest_author":"https://pith.science/pith/DIXEU7H4YPOWL6NI3Y45XADBMK/action/author_attestation","sign_citation":"https://pith.science/pith/DIXEU7H4YPOWL6NI3Y45XADBMK/action/citation_signature","submit_replication":"https://pith.science/pith/DIXEU7H4YPOWL6NI3Y45XADBMK/action/replication_record"}},"created_at":"2026-06-30T02:17:29.326646+00:00","updated_at":"2026-06-30T02:17:29.326646+00:00"}